If you are not a United States citizen any conviction can affect your status in the United States and could lead to the inability to get naturalized or even lead to deportation. It is imperative to speak with an attorney prior to pleading guilty to any charge if you are not a United States citizen.
Certain crimes are more detrimental to ones immigration status. For example, theft crimes and crimes involving moral turpitude are more likely to lead to deportation or an inability to become a naturalized citizen.
Also, aggravated felonies (violent crimes, sex crimes, etc) or felonies where you are incarcerated for more than a year will have a devastating to your immigration status.